[1S3-GS-2] Machine learning:

[1S3-GS-2-05] Categorical Interpretation of Algorithmic and Architectural Constraints of Deep Learning

〇Genji Ohara¹, Takashi Matsubara¹ (1. Hokkaido University)

Keywords:category theory, deep learning, G-equivariant convolutional neural networks

There have been many attempts to provide a mathematical foundation for deep learning, which has been driven by empirical design. In particular, many studies have been conducted to describe the properties of models as functoriality or naturality in category theory, but a framework that bridges these results has not been adequately provided. In this paper, we introduce a new perspective to overview these studies, aiming to provide a unified description of various categorical interpretations. We show that the category theory perspective can divide constraints on deep learning models into (i) algorithmic constraints, which the model is required to satisfy through learning, and (ii) architectural constraints, which the model is designed to satisfy before learning. Finally, we discuss the direction for a unified framework that integrates these two types of constraints.